Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents

TL;DR

This paper develops an exact kinetic theory for charge transport in out-of-equilibrium XXZ spin chains, providing explicit charge and current profiles and validating results with numerical simulations.

Contribution

It introduces a novel kinetic framework for elementary excitations in the XXZ chain, deriving exact charge and current profiles in non-equilibrium states.

Findings

Exact charge and current profiles derived for out-of-equilibrium XXZ chains.

Theoretical predictions match TEBD numerical simulations within error margins.

Provides an explicit formula for charge currents in stationary states.

Abstract

We consider the non-equilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought as the result of joining chains with different global properties. Through dephasing, at late times the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: 1) at different temperatures; 2) in the ground state of two different models; 3) in the "domain wall" state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on TEBD algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.